Construction of a set of circulant matrix submatrices for faster MDS matrix verification
This addresses a computational bottleneck in cryptography and coding theory for verifying MDS matrices, though it is an incremental improvement specific to circulant matrices.
The paper tackles the problem of efficiently verifying whether a circulant matrix is maximum distance separable (MDS) by constructing a smaller subset of submatrices to test for singularity, reducing the testing set size by approximately two matrix orders compared to the general method.
The present paper focuses on the construction of a set of submatrices of a circulant matrix such that it is a smaller set to verify that the circulant matrix is an MDS (maximum distance separable) one, comparing to the complete set of square submatrices needed in general case. The general MDS verification method requires to test for singular submatrices: if at least one square submatrix is singular the matrix is not MDS. However, the complexity of the general method dramatically increases for matrices of a greater dimension. We develop an algorithm that constructs a smaller subset of submatrices thanks to a simple structure of circulant matrices. The algorithm proposed in the paper reduces the size of the testing set by approximately two matrix orders.